Portfolio is a collection of things. For example, there are project portfolio, application portfolio, asset portfolio, investment portfolio, and others. Portfolio optimization selects portfolio elements to construct a solution that best achieves one or more quantitative objectives and to satisfy the required quantitative and inter-dependency constraints. Quantitative objectives and quantitative constraints are calculated based on portfolio element's attribute measurements. For example, investment oriented portfolio optimization determines an optimal investment ($X) on proposals ($Y, Y>>X) to best achieve the portfolio's economic measures considering proposal attributes including cost, consumption of resources, benefits, and inter-dependencies, and others.
Inter-dependencies can be logical dependencies or valuated dependencies. Logical dependency can be expressed as “require” or “exclude” types. For instance, “element A requires B” means that if A is selected, then B should also be selected; “element A excludes B” means that A and B cannot be selected together.
Valuated dependency is a kind of dependency among elements that will change the number of one or multiple involved elements' attributes. Valuated dependency may be further broken down into different types: for example, resource valuated dependency (RVD) which is explained as follows—suppose developing component A requires 30 person days, developing component B requires 40 person days, if there is a −10% RVD from A to B, then when A and B are developed together, the total resource consumption should be 30*(1-10%)+40=67 person days; duration valuated dependency (DVD) may be explained as follows—suppose developing component A requires working 20 days, developing component B requires 15 working days, if there is a +10% DVD from A to B, then when A and B are developed together, the total duration should be 20*(1+10%)+15=37 working days; benefit valuated dependency (BVD) may be explained as follows—suppose product A can bring benefit of 40,000 dollars after delivery, product B can bring benefit of 25,000 dollars after delivery, if there is a +10% BVD from A to B, then when A and B are delivered together, their total benefit should be 40,000*(1+10%)+25,000=69,000 dollars.
While the current portfolio optimization approaches may consider logical dependencies, they seldom consider valuated dependencies. A typical approach to enhancing existing portfolio optimization approaches that support logical dependencies to also support valuated dependencies, has been to modify the existing portfolio optimizer. However, such an approach poses several challenges: the complexity of understanding existing optimizer code, the complexity of cautious design for adding code to existing base, the risk of involving defects to original functions by dispersed modification on existing base, and the efforts and risk growing with increased valuated dependency types to be considered.